Real-time quantitative PCR is a method to quantify selected polynucleotide sequence by amplifying its initial concentration until well detectable level. The PCR reaction itself is almost an obligatory tool in every molecular biological laboratory and the principle behind this method was described in U.S. Pat. No. 4,683,195 (Mullis et al.) and U.S. Pat. No. 4,683,202 (Mullis). Real-time quantitative PCR induces amplification of nucleic acid amount in sample. This amplification is strongly non-linear and for simplification considered as exponential in its most progressive phase. The amplification of selected locus of DNA is achieved by repeated cycles of set temperature program that facilitates DNA replication by polymerase enzyme. The locus to be amplified is delimited by pair of primers that anneal to the template by molecular affinity and facilitate polymerization of new strand of DNA from supplied essential nucleotides by polymerase enzyme. Eventually, the finalized double stranded DNA product melts into two single stranded molecules by elevated temperature. To clearly separate and facilitates each of these fundamental steps, temperature regime is controlled and repeated in every cycle by the PCR thermal cycler. A recent embodiment of a thermal cycler is described in U.S. Pat. No. 5,455,175 (Wittwer et al.). The fundamental improvement from a qualitative towards quantitative method was facilitated by addition of fluorescence emitting agent into reaction mix whose fluorescence emission can be monitored throughout the reaction progress. Added into reaction, fluorescence emitting agent closely reflects the current concentration of the nucleic acid mass formed cycle by cycle by interacting with it (Higuchi et al., 1993). In this way, a trackable reaction kinetics trajectory is generated having a specific geometry. The signal emitted by interaction of signaling agent with reaction product is monitored once per cycle and when strengthened enough, the cycle number or its fraction is recorded at this threshold. In this way the so called threshold cycle (Ct) is obtained. To say when the threshold signal of an individual PCR has been reached, qualified arbitrary decision is made or a computing procedure is employed. Examples of such techniques are detailed in U.S. Pat. No. 6,303,305 (Wittwer et al.), WO 97/46707, WO 97/46712 and WO 97/46714 (Wittwer et al.).
Kinetics Compatibility
The herein claimed invention provide improvement to the verification of amplification kinetics compatibility between PCRs published by Bar et al. (2003, 2005) and Chervoneva et al (2006). The underlying concept of this method is based on the fact that any unwanted erroneous effect will primarily affect the amplification reaction kinetics visualized by the specific geometry of each PCR kinetics trajectory and only secondarily the amount of analyte calculated. Therefore, compatible amplification kinetics between PCRs to be compared is the elementary prerequisite of reliable results. The herein presented invention provides a method to achieve such comparison by comparing the PCR kinetics trajectories of the PCRs performed under investigations by analyzing their geometry and applying suitable metrics to facilitate statistical inference about similarity or heterogeneity of the compared trajectories. Only PCRs with comparable PCR kinetics trajectories can be considered compatible and hence suitable for quantitative determination of a DNA analyte.
Characterization of Amplification Kinetics
The amplification kinetics can be visualized by two-dimensional plot of signal measurements versus PCR cycle number. The full plot of all signal readings has sigmoid character, provided data from enough cycles are plotted. As discussed above, this is called the PCR kinetics trajectory.
Traditional approach to the PCR says that the PCR is a chain reaction progressing in a fashion close to perfect doubling. That is, every selected DNA molecule in reaction becomes a target template for synthesis of its one new complementary copy within one cycle of the polymerase reaction. Such an ideal doubling fashion of the PCR reaction can be described by the following model:P=T·(1+En); E→1  [1]where P is the PCR product measured after n cycles, T is the starting amount of the target sequence, E is the amplification efficiency expressed as the proportion of target molecules copied in PCR cycle (from 0, representing no amplification, to 1, representing the ideal doubling). Description of the reaction kinetics by the exponential models can be, however, considered as a simplification of the true nature of the reaction (Rutledge 2004). In fact, no non-discrete section of the reaction trajectory behaves really exponentially and with every cycle the efficiency declines (FIG. 1).
Several methods have been published describing methods of computing the amplification efficiency from the portion of the signal trajectory considered close to exponential. This portion was usually selected somewhere between the departure from the background phase and the entry into the plateau phase and consisted of some three to ten signal readings (Bar et al. 2003, Tichopad et al. 2003). Alternatively, selected portion was transformed by log of the signal values and fitted by linear model (Liu and Saint, 2002). This approach is, however, based on the same assumption of exponential amplification data which, after log transformation, become linear. In addition, selection of the portion to be fitted by the exponential model is done more or less arbitrarily and any shift down- or upwards affects the amplification efficiency calculated. What makes PCR kinetics even more complex is the interaction between the signal agent and the product formed. It was shown that this does not remain constant but rather changes with the reaction progress (Zipperet et al. 2004). Herein presented invention utilizes recent disclosures about the more complex amplification kinetics. With each cycle the efficiency decreases until it ceases completely in the plateau phase. Hence, the efficiency E from Equation 1 is instable and cycle-dependent. This largely invalidates its use alone as a metrics for reliable and robust geometric characterizing each PCR kinetics trajectory. The amplification kinetics can theoretically be broken down into two components, the growth component and the saturation component. Both components are present already in the first cycle, usually strongly in favor of the growth component. As the reaction progresses, the balance changes until the saturation component dominates over the growth. Such dynamics can be described by a model including more than one parameter of the kinetics. A good example is fitting the entire set of data by the following model (Tichopad et al., 2002), where the plateau height is the measure of saturation:
                              f          ⁡                      (            x            )                          =                              y            0                    +                      a                          1              +                              ⅇ                                                      -                                          (                                              x                        -                                                  x                          ⁢                                                                                                          ⁢                          0                                                                    )                                                        /                  b                                                                                        [        2        ]            The f(x) is the value of the function computed at cycle x, y0 is the background fluorescence, a is the difference between maximal and background fluorescence, e is the natural logarithm base, x0 is the x-coordinate of the inflexion point of the amplification curve, and b is a parameter reflecting the slope of the curve (FIG. 2).
The parameter a can be related to the saturation components whereas the parameter b is more strongly related to the growth component. If both taken simultaneously for characterization of the reaction kinetics, they add together more information about the amplification kinetics than each of them separately. Moreover, the parameters are not fully independent, in fact they are correlated. The direction and strength of the correlation is another contribution to the unique characterization of the kinetics.
Another multi-parametric characterization of the amplification kinetics can be reached by estimation of the amplification kinetics in several discrete points of the trajectory. Derived from equation [2], reaction-specific efficiency can be estimated from the predicted values f(x) at any cycle x by Equation [6]:
                              E          ⁡                      (            x            )                          =                                                            f                ⁡                                  (                                      x                    +                    1                                    )                                            -                              y                0                                                                    f                ⁡                                  (                  x                  )                                            -                              y                0                                              -          1                                    [        3        ]            
In this way, several parameters describing the amplification kinetics at different cycles along the trajectory can be obtained. Relying on only one efficiency estimate (e.g. at cycle 10) would provide only insufficient information about the entire reaction kinetics. Neither here the consecutive estimates of efficiency are fully independent, providing thus additional information via the strength and direction of the correlation.
Characterization of Kinetics by Covariance Matrix
The straightforward method to compare similarity of one kinetics parameter, is to log transform the data points in the exponential phase and test the similarity of the slopes of two curves by t-test (Payton 2004) or Zar's method (Gentle 2001). However, the relatively late stage the first clear signal is detected above the noise, and the smooth change of efficiency along the PCR causes to a difficulty in estimating the efficiency of compared PCRs exactly at the same phase of the reaction. Therefore, verification of compatibility based on parameters from plurality of reactions must be obtained. In such statistical design, the shape and size of multivariate data are described by the covariance matrix, a fundamental term in the linear algebra and multivariate statistics. It is a matrix of covariances between elements of vectors X an Y that represent here the kinetics parameters xi and yi for several reactions. Intuitively, covariance is the measure of how much two variables vary together. That is to say, the covariance becomes more positive for each pair of values which differ from their mean in the same direction, and becomes more negative with each pair of values which differ from their mean in opposite directions. In this way, the more often they differ in the same direction, the more positive the covariance, and the more often they differ in opposite directions, the more negative the covariance.
Utilized Disclosures
Bar et all (2003, 2005) and Chervoneva et al (2006) reported on methods of kinetics outlier detection among group of PCRs, employing defined reference set. In both methods, signal readings in the most progressive parts of the amplification trajectory were fitted with the exponential model and efficiency of the assumed exponential amplification was figured out. Subsequently, individual PCRs were compared statistically with defined reference and PCRs with significantly outlying efficiency values were recommended for exclusion. Both methods, in despite of their designation, in fact ignored the kinetics of the amplification, which is characterized by substantial decay of the amplification efficiency with every cycle, an assumed rather constant efficiency in the fitted region. The major shortcoming of these methods is that selecting a particular data points along the trajectory for the exponential fit affects the efficiency obtained, and thus the resolution between different PCRs.
Tichopad et al employed the four parametric sigmoid model (Equation [2]) to describe and compare amplification performances on different reaction substrate manipulated by primer selection (2002), different extraction residua (2004) and added inhibitor (2005). In this way, conclusion could have been drown from the experimental set-up on an effect of minute reaction disturbance on the reaction performance. The comparison of reaction was performed by means of statistical tests that compared individual parameters obtained from the fitted model one by one between groups of PCRs. This approach might show an effect of minute contaminations among reaction set-ups on the steepness of the reaction trajectory as described by the parameter b (FIG. 2) or on the height of the amplification curve as described by parameter a. Such approach provided user with the possibility to validate comparability of groups of PCRs where heterogeneous reaction conditions are assumed. This however was not within the focus of the cited works. The focus rather was only to show that there is an effect of added compounds (Tichopad 2004, 2005) or residua (2004) on the kinetics. Interestingly, both indicators of performance a and b were distinctly affected by the contaminants and not always alleged the same conclusion. Considering this, drawing conclusion on kinetics heterogeneity among PCRs could be impossible where conflicting outcomes from both parameters would be obtained. For this reason, comparison based on a single parameter might not be suited to draw numerically supported decision on compatibility among PCRs.
Quantification of nucleic acid in sample from obtained maximum of defined derivative of smoothed signal readings is described in U.S. Pat. No. 6,303,305 (Wittwer et al., 2001). The said invention is based on assumed relation between the geometric shape of the amplification curve, as characterized by the maximum of, for instance, second derivative, and the initial amount of nucleic acid. In herein claimed invention the plurality of n-th derivative maxima is used not to quantify nucleic acid amount, but to facilitate comparison of amplification curves between reactions.